Bornhuetter–Ferguson / Benktander / Cape Cod
Blend a-priori expected losses with emerged experience via BF, its iterated Benktander form, and the data-driven Cape Cod method, side by side with chain-ladder.
Loaded: United Services Automobile Asn Grp — Private Passenger Auto (paid, CAS Loss Reserve DB)
| Origin \ Dev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
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Premium by origin year & expected loss ratio
Ultimate comparison
| Origin year | CL ultimate | BF ultimate | Benktander ultimate | Cape Cod ultimate |
|---|---|---|---|---|
| AY 1 | 886,334 | 886,334 | 886,334 | 886,334 |
| AY 2 | 982,932 | 982,148 | 982,931 | 982,148 |
| AY 3 | 1,079,102 | 1,075,537 | 1,079,090 | 1,075,537 |
| AY 4 | 1,146,697 | 1,138,375 | 1,146,637 | 1,138,375 |
| AY 5 | 1,246,146 | 1,226,650 | 1,245,841 | 1,226,650 |
| AY 6 | 1,375,073 | 1,324,732 | 1,373,230 | 1,324,732 |
| AY 7 | 1,440,528 | 1,320,130 | 1,430,466 | 1,320,130 |
| AY 8 | 1,430,755 | 1,185,300 | 1,388,645 | 1,185,300 |
| AY 9 | 1,455,908 | 966,162 | 1,291,165 | 966,162 |
| AY 10 | 1,568,804 | 542,021 | 896,774 | 542,021 |
IBNR comparison
| Origin year | CL IBNR | BF IBNR | Benktander IBNR | Cape Cod IBNR |
|---|---|---|---|---|
| AY 1 | 0 | 0 | 0 | 0 |
| AY 2 | 784 | 0 | 783 | 0 |
| AY 3 | 3,565 | 0 | 3,553 | 0 |
| AY 4 | 8,322 | 0 | 8,262 | 0 |
| AY 5 | 19,496 | 0 | 19,191 | 0 |
| AY 6 | 50,341 | 0 | 48,498 | 0 |
| AY 7 | 120,398 | 0 | 110,336 | 0 |
| AY 8 | 245,455 | 0 | 203,345 | 0 |
| AY 9 | 489,746 | 0 | 325,003 | 0 |
| AY 10 | 1,026,783 | 0 | 354,753 | 0 |
| Total | 1,964,890 | 0 | 1,073,724 | 0 |
IBNR by method
Assumptions & limitations
- Premium is on-level (rate and mix adjusted) so that a single expected loss ratio is meaningful across origin years.
- The a-priori expected loss ratio is a credible, independent estimate (e.g., pricing plan or industry benchmark) — not derived from the same data being reserved.
- Cape Cod pools all origin years to estimate a single ELR from the data; it will differ from a manually chosen BF a-priori.